Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21458223 | C2 | semidirect |
| 2. #21448098 | C2 | semidirect |
| 3. #21448008 | C2 | semidirect |
| 4. #21447998 | C2 | semidirect |
| 5. #21447976 | C2 | semidirect |
| 6. #21447919 | C2 | semidirect |
| 7. #21447652 | C2 | semidirect |
| 8. #21447604 | C2 | semidirect |
| 9. C4×D16×C61 | C2 | semidirect |
| 140. C4×D16 | D61 | semidirect |
| 173. C61 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458223 | 2 |
| #21448098 | 2 |
| #21448008 | 2 |
| #21447998 | 2 |
| #21447976 | 2 |
| #21447919 | 2 |
| #21447652 | 2 |
| #21447604 | 2 |
| C4×D16×C61 | 2 |
| #33922 | 61 |